6.2 Review

6.2 Review

The Converse of the Pythagorean Theorem

Using the converse of the Pythagorean Theorem

Is a triangle with sides 6, 8, and 12 a right triangle?

6² + 8² = 12²

36 + 64 = 144

100 = 144

100 does not equal 144, therefore, it is NOT a right triangle.

Multiple Choice

Is a triangle with sides 6, 8, and 10 a right triangle?

• No, because

  6 + 8 ≠ 10

• Yes, because

  6² + 8² > 10²

• Yes, because

  6² + 8² = 10²

  36 + 64 = 100

  100 = 100

Multiple Choice

Is a triangle with sides 5, 8, and 12 a right triangle?

• No, because

  5² + 8² = 12²

  25 + 64 = 144

  89 ≠ 144

• Yes, because

  5² + 8² < 12²

• No, because

  5 + 8 ≠ 12

Pythagorean Triples

A set of positive integers that satisfies the Pythagorean Theorem, a² + b² = c².

Multiple Select

Which of the following is a Pythagorean Triple? (Check all that apply)

• (3, 4, 5)

• (5, 12, 13)

• (7, 8, 12)

• (6, 8, 10)

• (2, 3, 4)

Procedure to show the converse of the Pythagorean Theorem in action!

You are given sides 5 cm, 9 cm, 12 cm, and 13 cm.

Step 1: Determine which of these make a Pythagorean Triple.

**5, 12, and 13.

Step 2: Write a true statement using the Pythagorean Theorem and your side lengths. Describe in words as well.

** Since 5² + 12² = 13², you would draw the 5 cm side and the 12 cm side with a right angle between them. The 13 cm side will fit to form a right triangle.

Multiple Choice

Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 3 feet, 4 feet, 5 feet, and 6 feet.

• Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The 5-foot side will fit to form a right triangle.

• Knowing that 3² + 4² = 5², draw any two of the sides with a right angle between them. The third side will fit to form a right triangle.

• Knowing that 3² + 5² ≠ 6², draw the 3-foot side and the 5-foot side with a right angle between them. The 6-foot side will fit to form a right triangle.

Multiple Choice

Select the procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 6 cm, 9 cm, 12 cm, and 15 cm.

• Knowing that 6² + 12² ≠ 15², draw the 6 cm side and the 12 cm side with a right angle between them. The 15 cm side will fit to form a right triangle.

• Knowing that 9² + 12² = 15², draw any two of the sides with a right angle between them. The third side will fit to form a right triangle.

• Knowing that 9² + 12² = 15², draw the 9 cm side and the 12 cm side with a right angle between them. The 15 cm side will fit to form a right triangle.